Answer:
height = 4
Step-by-step explanation:
b = 3h
b * h = 48
3h * h = 48
3h² = 48
3/3 h² = 48/3
h² = 16
h = √16
h = 4
b = 4 * 3
b = 12
The near model represents the height, f(x), of a water batson thrown off the root of a building over time, x, measured in seconds
Part A During what intervals) of the domain is the water batoon's height increasing? Of points)
Part B: During what interval) of the domain is the water baloon's height staying the same? (2 points)
Part C: During what intervale) of the domain is the water batoon's height decreasing the fastest? Use complete sentences to support your answer. ( points)
Part D: Use the constraints of the real world situation to predict the height of the water beloon at 14 seconds. Use complete sentences to support your answer (3 points)
A) During the interval (0, 2) of the domain the water balloon's height is increasing.
B) During the interval (2, 4) of the domain the water balloon's height is staying the same.
C) During the interval (8, 10) of the domain, the water balloon's height is decreasing the fastest.
D) The height of the balloon will be zero since the height of the balloon has remained the same from the 10th interval.
What is an interval?
In mathematics, an interval is quantified in terms of numbers. Every number between two specific integers is considered to be an interval. Between those two values, this range encompasses all real numbers. Real numbers can be of any type you can imagine.
All the numbers between a pair of provided numbers are considered an interval. It is crucial to indicate if the start and end numbers are included. The Number Line, Inequalities, and Interval Notation are the three primary methods for displaying intervals.
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Marely has a picture frame that is 6 inches long and 5 inches wide.
They have a second frame that has the same length, and a width
that is 2 times as much as the first one.
What is the area of the second frame?
Answer:
60 square inches
Step-by-step explanation:
The width of the second frame is 2 times the width of the first frame, or 2 * 5 inches = 10 inches.
The area of the second frame is its length multiplied by its width, or 6 inches * 10 inches = 60 square inches.
0.23 was rounded to 2 significant figures.
What is the upper bound?
Answer: 0.235
Step-by-step explanation:
To round up you need a number = 5 or > 5
So to round to 2 sig fig, the number will have to be 0.235
Im having trouble..
i keep on getting this question wrong and i need help with the answer, i need to get a high score on this assignment so i can move on
Answer:
The rate of change is also called the slope. The slope is -2
Step-by-step explanation:
Find 2 points on the line. I am going to use the points (0,5) and (4, -3). the rate is the change in y over the change in x. From the two points, my values are -3 and 5. The x values are 4 and 0.
To find the change, I subtract the y values and the x values.
[tex]\frac{-3-5}{4-0}[/tex] = [tex]\frac{-8}{4}[/tex] = -2
Answer: -2
Step-by-step explanation: The rate of change is also known as the slope!
To find the slope, you need to find the rise/run.
Let's pick two points ( 0,5) ( 4, -3)
You see that the y goes down by 8 and the x goes right by 4, so the rate of change is -8/4 = -2
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Please help with this problem!!
Functions f, g, and h are defined as follows: () = − 2, () = 2^2 − 1, and ℎ() =
2^3 + 4.
(a) Find the inverse of function g(x).
(b) Find f(h(-2))
(c) Find g(f(5))
Answer:
Step-by-step explanation:
f −1 (x)= 3x−2
f, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis, equals, start fraction, x, minus, 2, divided by, 3, end fraction.
show steps / why your answer is correct please which equation defines the graph of y=x3 after it is shifted vertically 5 units down and horizontally 4 units left
The equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.
What is a graph?A function is truly equal to its graph in the modern mathematical foundations and typically in set theory. However, it is frequently helpful to think of functions as mappings, which include not just the relationship between input and output but also the sets that make up the domain and codomain. For instance, it is important to consider the codomain while determining whether a function is onto (surjective) or not.
For k=- 5, y=f(x) + k represents a vertical shift down.
For h=4, the horizontal shift left is y=f(x+h).
Therefore, the equation that defines the graph y=x³ after it is shifted vertically 5 units down and horizontally 4 units left is y =( x + 4 )³- 5.
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Answers and Explain
The function g(x) is a piecewise function For x 4, 1 g(x) = |x + 1| and for
x 1, 3 g(x) = 2.
What are some rules for the transformation of functions?Suppose we have a function f(x).
f(x) ± d = Vertical upshift/downshift by d units (x, y ±d).
f(x ± c) = Horizontal left/right shift by c units (x - + c, y).
(a)f(x) = Vertical stretch for a > 0, vertical shrink a < 0. (x, ay).
f(bx) = Horizonatal compression b > 0, horizontal stretch for b < 0. (bx , y).
f(-x) = Reflection over the y-axis, (-x, y).
-f(x) = Reflection over x-axis, (x, -y).
From the graph, we can conclude that g(x) is a piecewise function.
When x is - 4, 1 g(x) = |x + 1|.
And when x is 1, 3 g(x) = 2, A constant function.
Now, g(-2) = | - 2 + 1| = 1.
g(1) = | 1 + 1| = 2.
g(4) = 2.
The value of x when g(x) = 3 is - 4.
The value of x when g(x) = 1 is (0, - 2) as both satisfy g(x).
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CAN ANYONE PKEASE HELP MEEEEEE
Answer: y = 10(x) + 56
Step-by-step explanation:
y=10(4) + 56
y = 40 + 56
y = 96
Answer:
1a. y = 10 x + 16
1b. 16
2a. y = 600x + 1500
2b. $8700
Step-by-step explanation:
1a. A linear model represents a relationship between two variables as a straight line. In this case, we want to represent the relationship between the number of hours a canoe is rented for and the total cost of the rental, including the deposit.
We can create a linear model by using the equation y = mx + b, where y is the total cost, x is the number of hours the canoe is rented for, m is the slope of the line (the rate at which the cost changes per hour), and b is the y-intercept (the total cost when x is 0).
Since the total cost includes a non-refundable deposit, we need to add this to the y-intercept. The deposit is not dependent on the number of hours the canoe is rented for, so it is not represented in the slope.
Based on the information given, the total cost is $56 when the canoe is rented for 4 hours, and the rental fee is $10 per hour. We can use these values to solve for the y-intercept and the slope:
y = mx + b
56 = (10) (4) + b
56 = 40 + b
b = 56 - 40
b = 16
So the linear model representing the relationship between the number of hours a canoe is rented for and the total cost of the rental, including the deposit, is: y = 10 x + 16
1b. We know that the total cost is $56 when the canoe is rented for 4 hours, and the rental fee is $10 per hour. We can use these values to solve for the y-intercept, which represents the non-refundable deposit:
y = (10) (4) + b
56 = 40 + b
b = 56 - 40
b = 16
So the non-refundable deposit is $16. This means that the total cost of the rental, including the deposit and the hourly fee, is $56.
2a. We can create a linear model by using the equation y = mx + b, where y is the total cost, x is the number of solar heaters produced, m is the slope of the line (the rate at which the cost changes per heater), and b is the y-intercept (the total cost when x is 0).
Based on the information given, it costs $7500 to produce 10 solar heaters, and it costs $13,500 to produce 20 solar heaters. We can use these values to solve for the y-intercept and the slope:
y = mx + b
7500 = m(10) + b
13500 = m(20) + b
Subtracting the second equation from the first equation gives:
-6000 = m(10) - m(20)
6000 = m(20) - m(10)
6000 = m(20 - 10)
6000 = m(10)
m = 6000/10
m = 600
Substituting this value for m in either of the original equations and solving for b gives:
7500 = (600)(10) + b
7500 = 6000 + b
b = 7500 - 6000
b = 1500
So the linear model representing the relationship between the number of solar heaters produced and the total cost of production is:
y = (600) x + 1500
According to this model, the total cost of producing 15 solar heaters would be $10,500.
2b. To find the total cost of producing 12 solar heaters, we can use the linear model that represents the relationship between the number of solar heaters produced and the total cost of production:
y = (600) x + 1500
Where y is the total cost, x is the number of solar heaters produced, m is the slope of the line (the rate at which the cost changes per heater), and b is the y-intercept (the total cost when x is 0).
To predict the total cost of producing 12 solar heaters, we can substitute 12 for x in the equation:
y = (600) (12) + 1500
y = 7200 + 1500
y = 8700
According to this model, the total cost of producing 12 solar heaters would be $8700.
HELP! ASAP! 15 PTS!
the expression quantity negative three fifths times x minus 7 end quantity minus quantity negative 12 plus three tenths times x end quantity
1. negative nine tenths times x plus 5
2. negative nine tenths times x plus negative 5
3. three over 10 times x plus 5
4. three over 10 times x plus negative 19
The expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or (-3 1/4d + 3/5) - (2 7/8d + 7/10) is equivalent to "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.
An algebraic expression is a number, variable, or the combination of both and operational symbols.
To determine the equivalent of the expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or simply (-3 1/4d + 3/5) - (2 7/8d + 7/10), combine all like terms and perform the necessary operations.
(-3 1/4d + 3/5) - (2 7/8d + 7/10)
⇒ -3 1/4d + 3/5 - 2 7/8d - 7/10
⇒ (-3 1/4 - 2 7/8)d + 3/5 - 7/10
⇒ (-13/4 - 23/8)d + 6/10 - 7/10
⇒ (-26/8 - 23/8)d - 1/10
⇒ -49/8 d - 1/10
Hence, the equivalent expression is "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.
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A small country emits 150,000 kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by 5.4% per year for the next 14 years. In the first year of the agreement, the country will keep its emissions at 150,000 kilotons and the emissions will decrease 5.4% in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the 14 year period, to the nearest whole number?
Answer:
72891
Step-by-step explanation:
150,000 is the base number
In the first year it will be the same, so it'll only count 13 years
the equation is: 150,000(0.946)^x
how:
150,000(100%-5.4%)^x
150,000(94.6%)^x
150,000(0.946)^x
*it's 100%-5.4% because that's that's remaining each year if it's decreasing by 5.4%. you would convert the percentage into decimals because it's decreasing by a percentage, not a whole number
150000(0.946)^13
*13 is the number of years, so it's x
72891.356467
18.
Kara solved the following absolute value equation incorrectly. Find and fix her
mistake. Explain what she did wrong.
|- 2x + 6 + 10 = 2
-10 -10
2x+6=-8
-6 -6
-2x = -14
-2
-2
X = 7
|- 2x + 61
{7, - 1}
= -8
2x+6=8
-6 -6
-2x = 2
-2 -2
x = -1
Kara erred when she answered the equation 2x + 6 = -8. Instead, she should have solved the equation 2x + 6 = 8 because it relates to the second situation (where -2x + 6 + 10 is smaller than 0).
Kara made a mistake when solving the equation |- 2x + 6 + 10| = 2. The correct steps to solve this equation are as follows:
First, we need to find the value of -2x + 6 + 10. To do this, we need to remove the absolute value bars by considering two cases:
a. If -2x + 6 + 10 is greater than or equal to 0, then the absolute value is equal to -2x + 6 + 10.
b. If -2x + 6 + 10 is less than 0, then the absolute value is equal to the negative of -2x + 6 + 10.
In the first case, we have -2x + 6 + 10 = 2. Solving this equation gives us x = -1.
In the second case, we have -(-2x + 6 + 10) = 2. Solving this equation gives us x = 7.
Therefore, the solution to the equation |- 2x + 6 + 10| = 2 is x = {7, -1}.
She made a mistake when she solved the equation 2x + 6 = -8. She should have solved the equation 2x + 6 = 8 instead, because this is the equation that corresponds to the second case (where -2x + 6 + 10 is less than 0).
As a result, Kara got the wrong value for x and included the incorrect solution {7, -1} in her final answer.
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Pls help 8th grade math
Answer: 27.5, B
Step-by-step explanation:
its a right angled trianalgle,
==> (30)^2= ((12)^2)+(x^2)
==> x^2= 900-144
==> x^2 = 765
==> x=(756)^(0.5)
==> x=27.49
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pls help me, i need this done very soon.
Answer: for 35x+21 the answer is 7(5+3)
for the second one, the answer is 4x+2x+2
the 3rd one the answer is 5(6-3x)
for the fouth one the answer is 40x+50
for the fifth one the answer is 4x+4x+3
Step-by-step explanation:
I think this is an elimination problem:
12x-20y=-32
x+20y=10
Answer:
Yup I think so to
Step-by-step explanation:
Answer:
Yes, it is an elimination problem.
x = -1.69230769
Step-by-step explanation:
You can eliminate 20y by adding both equations together.
Then, you will get 13x = -22.
Divide by 13 on both sides to get x= -1.69230769
Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Jose's account went into overdraft. To get back to a positive balance, he deposited money at a steady rate of $31.97 per week. After 3 weeks, he had $47.3 in the account. What was the balance when the account went into overdraft?
The balance when the account went into overdraft was -48.61
What is an overdraft?An overdraft occurs when something is withdrawn in excess of what is in a current account. For financial systems, this can be funds in a bank account.
Let x be the balance when the account went into overdraft
To get back to a positive balance he deposited money at a steady rate of $31.97 per week.
Amount deposited per week = $31.97
Amount deposited 3 weeks = $95.91
Now amount in account after 3 weeks =x+95.91
We are given that After 3 weeks, he had $95.91 in the account.
So, x+95.91=47.3
x= 47.3-95.91
x= -48.61
Hence The balance when the account went into overdraft was -48.61
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pls help due tomm!! super easy
Answer:8a<8b
Step-by-step explanation:
8a<8b
Help I do not understand this problem. 1/5 of this number is 2/5
Answer:2.
2/5 times 5 is 10/5 or 2
Step-by-step explanation:
To solve the equation t² - t = 12 by factoring, you would use
(t - 4)(t + 3) = 0
t(t - 1) - 12 = 0
t(t - 1) = 12
To solve the given equation, t² - t = 12, by factoring, we will use (t + 3)(t - 4) = 0. The correct option is the first option
Solving an equation by factoringFrom the question, we are to determine how to solve the given equation by factoring
From the given information,
The given equation is
t² - t = 12
First, we will solve the equation by factoring
t² - t = 12
Transfer the constant to the other side
t² - t - 12 = 0
Factorize the expression
t² -4t + 3t - 12 = 0
t(t - 4) +3(t - 4) = 0
(t + 3)(t - 4) = 0
Then,
t + 3 = 0 OR t - 4 = 0
t = -3 OR t = 4
Hence, to solve the equation we will use (t + 3)(t - 4) = 0
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Please help:
the congruence statements ∆ABC ≅ ∆DEF, ∆ABC ≅ ∆EFD and ∆ABC ≅ ∆FDE all are valid. what must be true about ∆ABC and ∆DEF
Find the constant of variation and the missing value when y varies directly with x.
If y = 35 when x = 7, find x when y = 49.
Answer:
42
Step-by-step explanation:
A right triangle has legs of 30 inches and 40 inches whose sides are changing. The short leg is increasing by 5 in/sec and the long leg is shrinking at 7 in/sec. What is the rate of change of the hypotenuse?
That is a change in the hypotenuse's length of -2.6 inches per second.
What in math is a rate?
A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. This ratio compares two dissimilar units: ounces and cents
h = sqr(b^2 + a^2), b=30, a=40, b'=-5, a'=-7
h' = [(1/2)/sqr(b^2+a^2)](2bb' + 2aa') = sqr(30^2+40^2)(30(5)+40(-7)
= (150-280)/sqr2500 = (-130)/50 =-- -13/5 = -2.6 inches per second
2.6 inches are lost from the hypotenuse every second.
Check the response by observing what transpires in one second.
30 to 35 on the short leg
greater leg descends from 40 to 37
From 50 to 47.4 is the hypotenuse
In one second, 50-47.4 equals a 2.6 reduction. That is a change in the hypotenuse's length of -2.6 inches per second.
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factor out using the gcf 1/5c + 4/5
The factored expression of 1/5c + 4/5 is 1/5(c + 4)
How to factor the expression?From the question, we have the following parameters that can be used in our computation:
1/5c + 4/5
From the above expression, we have the following highlights
Terms of the expressions = 1/5c and 4/5Number of terms = 2In the above terms, we can see that the denominator of the terms is 5
When this denominator is removed, we have
Expression = c + 4
This means that
GCF =1/5
So, the factored expression is 1/5(c + 4)
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In a tudy of pain reliver, 50 people were given product A, and 38 experienced relief. In the ame tudy, 100 people were given product B, and 90 experienced relief
In linear equation, { 2x + 3y = 7.20 , { 4x + 2y = 8.80 the price per pound for oranges.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Product B performed worse in the study because 32% failed to get relief with this product, whereas only 28% failed to get relief with Product A.
Working through this, the percentage who failed to find relief from product A is (25 - 18) / 25 = 28%. Doing the same type of calculation for product B, we can determine the percentage who failed to find relief as (50 - 34) / 50 = 32%. The description statement asks for which offered less relief, which we can find using the less than operator:
28% < 32%
Product A offered relief to all but 28% of the people, while product B offered relief to all but 32% of the people. Given that fewer people failed to find relief on product 28%, we can argue that more people did find relief on product A.
Given that the tests are both on multiples of 25 people, we can also see the percentages by multiplying the numerators and denominators to bring both to a scale of 100:
7/25 * 4/4 = 28% of product A users failed to find relief.
16/50 * 2/2 = 32% of product B users failed to find relief.
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the dilation of a line segment creates a _[blank]_ line segment, provided the center of dilation is not on the line segment and the scale factor does not equal 1.
The required scale factor for the given line segment is 2.
What is line segment?
In math, a line segment is limited by two unmistakable focuses on a line. Or on the other hand we can say a line portion is essential for the line that interfaces two focuses. A line has no endpoints and broadens endlessly in both the bearing yet a line fragment has two fixed or positive endpoints.
Explain scale factor:Scale factor is the number used to duplicate one item by to get another item that appears to be identical however is an alternate size. It makes a precise duplicate just bigger or more modest than the first. Scale Variable increases the image or item similarly as though you broadened or shrank it on a copier.
According to question:We have,
QS : QS' = 4 : 8 = QU : QU' = 5 : 10 = 1 : 2
Then the scale factor is of the dilation is 2 (magnification)
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The interior angles in a regular polygon sum to 1620°.
How many sides does the polygon have?
Answer:
the answer to your question is 11
Step-by-step explanation:
1620÷180= 9
9+2=11
Simplify, using the distributive
property.
18y - 13y = (18 - 13)y = [?] y
Using the distributive property we get 5y.
What is distributive property?
The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical characteristics that is utilised the most. Commutative and associative qualities are the other two important features.
This property states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend by the number separately and then adding the results together.
Using the distributive property
18y - 13y = (18 - 13)y
(18-13) y
Subtract the numbers: 18-13=5
=5 y
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The base of parallelogarm is 13 yards and the height is 10 yards what is the area
The parallelogram's area is 130 yards square.
What is unitary method ?Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.
Create a square on paper by using a pencil. Tw dimensions make it up. A shape's area on paper is the space it takes up.
Imagine that your square is made up of smaller unit squares.
The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.
To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.
According to our question-
base*height
base=13
height=10
13*10
= 130 yds
Hence, The parallelogram's area is 130 yards square.
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Solve the equation 3x+1=4x-8 for x.
Answer:
ok
Step-by-step explanation:
3x+1=4x-8= -6
x=-6
this is the x
I hope you have understand
reuben's coffee shop makes a blend that is a mixture of two types of coffee. type a coffee costs reuben $4.10 per pound, and type b coffee costs $5.35 per pound. this month's blend used four times as many pounds of type b coffee as type a, for a total cost of $586.50. how many pounds of type a coffee were used? numberofpoundsoftypeacoffee:
23 pounds of type A coffee were used and 92 pounds of type B coffee were used, using the concept of formula equation we get -
What is formula equation?A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.
Let assume that, x represent the number of pounds of type A coffee that were used in the blend.
and y represent the number of pounds of type B coffee that were used in the blend.
Type A coffee costs Lena $4.10 per pound, and type B coffee costs $5.35 per pound.
The total cost of the mixture is $586.50.
Now,
4.10x + 5.35y = 586.50 ............ (i)
This month's blend used four times as many pounds of type B coffee as type A.
so, y = 4x
Substituting y = 4x into equation (i), we get -
4.10x + 5.35 × 4x = 586.50
or, 4.10x + 21.4x = 586.50
or, 25.5x = 586.50
or, x = 586.50/25.5
or, x = 23
Next, y = 4x = 4 × 23
y = 92
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Sarah placed 3 identical wooden boards end - to - end. The length is 1.86 m. What is the length of each board?
Answer:
0.62
Step-by-step explanation:
1.86 divided by 3 is 0.62